1)A secret operation carried out by the Fight Club, led by Tyler Durden, to topple the corporate american system. Project Mayhem is an ongoing struggle against the power hungry rich bastards who don't give a fuck about the white coller working class american people.

2) A unique and better way of looking at life

1) blow up credit card buildings, reset the debt to zero

2a) In Tyler we trusted....
2b) On a long enough timeline, the survival rate for everyone drops to zero

In Fight Club, an operation headed by Tyler Durden that evolved from Fight Club. It's purpose, which is mentioned in the movie and made very clear in the book, is the complete destruction of civilation.

"We're going to break up civilation so we can make something better with the world" --- space monkey